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Suspension platform interferometer for the AEI

10m prototype: concept, design and optical layout

K Dahl1, O Kranz1, G Heinzel1, B Willke1, K A Strain1,2,

S Goßler1 and K Danzmann1

1 Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) andInstitut für Gravitationsphysik, Leibniz Universität Hannover, 30167 Hannover,Germany2 SUPA School of Physics & Astronomy, University of Glasgow, Glasgow, G128QQ, United Kingdom

E-mail: katrin.dahl@aei.mpg.de

Abstract.At present a 10m prototype interferometer facility is being set up at the AEI

Hannover. One unique feature of the prototype will be the suspension platforminterferometer (SPI). The purpose of the SPI is to monitor and stabilise therelative motion between three seismically isolated optical tables. The in-vacuumtables are suspended in an L-shaped configuration with an arm length of 11.65m.The design goal of the SPI is to stabilise longitudinal differential displacements toa level of 100 pm/

√Hz between 10mHz and 100Hz and relative angular noise of

10 nrad/√Hz in the same frequency band. This paper covers the design aspects

of the SPI, e.g. cross-coupling between the different degrees of freedom and fibrepointing noise are investigated. A simulation is presented which shows that withthe chosen optical design of the SPI all degrees of table motion can be sensed ina fully decoupled way. Furthermore, a proof of principle test of the SPI sensingscheme is shown.

PACS numbers: 07.60.Ly, 42.15.Eq, 04.80.Nn

Submitted to: Class. Quantum Grav.

1. Introduction

The AEI 10m prototype interferometer [1] aims not only at testing and developing newtechniques for future upgrades of gravitational-wave detectors, it is also a testbed forultra-low displacement noise experiments such as to measure the standard quantumlimit of interferometry or performing tests for the GRACE follow-on experiment [2].The prototype has an L-shaped vacuum envelope with an arm length of about 10m. Ateach end and in the corner of the ‘L’ a tank is located, housing a 1.75m× 1.75m opticaltable supported by a seismic attenuation system derived from the HAM-SAS table [3].Although these tables have been designed to provide excellent seismic isolation, therewill still be a certain amount of residual motion between the three tables. The taskof the suspension platform interferometer (SPI) is to sense this relative motion and

http://arxiv.org/abs/1201.4718v1

Suspension platform interferometer for the AEI 10m prototype 2

to allow suppression by actuators which are part of the seismic attenuation system ofeach optical table.

One of the planned experiments is to perform tests for a GRACE follow-onmission. GRACE [4] consists of two satellites, its goal is to map the Earth’s gravityfield. The orbital motion of each satellite senses local variations of the Earth’s gravityfield. This leads to small fluctuations of the inter-satellite distance. In order totest laser interferometers for GRACE follow-on missions, it is planned to performexperiments within the AEI 10m prototype where the suspended tables representsatellites. By using signals of the SPI, the tables will be moved on purpose by a well-known amount. This experiment sets the design goal for the SPI in the lower frequencyrange, which is less than 100 pm/

√Hz between 10mHz and 100Hz for longitudinal

table motion and 10nrad/√Hz for angular noise in the same frequency band.

The main experiment that will be set up on the tables of the AEI 10m prototypefacility is a Michelson interferometer with Fabry-Perot arm cavities. The scopeof this interferometer is to probe at and beyond the standard quantum limit ofinterferometry [5]. Therefore, all classical noise sources, e.g. seismic noise, have tobe sufficiently reduced to leave the sensitivity exclusively limited by quantum noisein the measurement band of interest. A straightforward way to reduce seismic noiseis to suspend all optics of the interferometer. The SPI and the table position controlact to reduce the relative motion of the tables, and hence stabilises the suspensionpositions of the suspended interferometer components that are supported by the tables.This stabilisation decreases the required force and hence the noise of the voice coilactuators that are an integral part of the position control of each suspension. Thereduced relative velocity of the components also makes it easier for the interferometercontrol system to acquire lock.

2. Introduction to suspension platform interferometry

The idea to set up an ancillary interferometer beside the main interferometer toimprove lock acquisition and the operation of the main interferometer, especially atlow frequencies, was proposed by Drever [6]. He suggested to install and lock anancillary interferometer at the intermediate stage of the suspended mirrors of themain interferometer to reduce their residual rms motions. This idea was tested byAso et al [7]. They measured 40 dB noise reduction between 0.1Hz and 1Hz. Inan experiment conducted by Numata and Camp [8], the relative longitudinal andyaw motions between two hexapods separated by 1m were measured by use of threehomodyne Michelson interferometers. The longitudinal displacement was stabilised to1 nm/

√Hz at 1mHz.

The SPI described in this paper is unique in the sense that

• the SPI will monitor the relative motion between three suspended optical tables(weight of about 1 t each and separated by about 10m).

• the SPI will provide continuous error signals over a wide (≫λ) operating rangeto track the relative table motions.

• the SPI will sense all degrees of freedom except for roll around the beam axis.Several optical configurations can be used to sense relative motions between two

objects, e.g. a Fabry-Perot cavity or an optical configuration using a pseudo-randomnoise code [9, 10]. The advantage of a Fabry-Perot cavity is that it is a fairly simplesetup. The main disadvantage and the reason why it was not an option for the SPI

Suspension platform interferometer for the AEI 10m prototype 3

is the limited sensing range of one cavity linewidth. We decided to use heterodyneMach-Zehnder interferometry to monitor the relative motions of the three suspendedtables. This provides the desired constant sensing performance at any table positionover many optical wavelengths. Furthermore, we are able to benefit from in-houseexperience gained with the experiments for LISA Pathfinder [11].

The optical layout of the SPI is shown in figure 1. It is the result of simulationwork taking into consideration several requirements. In this paper the layout ispresented first, followed by details of the simulation from which it resulted.

The following nomenclature is used in this paper: all photodiodes are abbreviatedwith PD followed by another letter that indicates to which interferometer thephotodiode belongs (D for diagnostic, R for reference, S for south, and W for west).All beam splitters are abbreviated with BS, all beam recombiners with BR, and allmirrors with M. All optics are placed on the central table except for mirror MS whichis placed on the south table and mirror MW which is placed on the west table. Thereference beam ”beamR” is confined to the baseplate on the central table, while partsof the measurement beam ”beamM” also travel to the south and west tables.

3. Optical layout

The SPI consists in total of four non-polarising heterodyne Mach-Zehnderinterferometers. All interferometers share the same optical path on the modulationbench, which is shown in the lower left box of figure 1. Here, the laser beam isprepared and coupled into optical fibres. The fibre outcouplers are mounted on themeasurement bench located on the central table inside the vacuum system. In contrastto the modulation bench which uses conventional optical mounts, the measurementbench is quasi-monolithic and thus much more stable in terms of mechanical andthermal drifts. All displacement measurements are performed on the measurementbench.

3.1. Modulation bench

The modulation bench housing the laser is located outside of the vacuum system.We choose to work with a continuous-wave laser of a wavelength of 1064nm and aimto reduce the SPI sensing noise due to laser frequency fluctuations to 10 pm/

√Hz at

10mHz, to make sure that laser frequency noise will not limit the SPI sensitivity. Sincethe arm length mismatch of two of the four Mach-Zehnder interferometers is about23m, the laser frequency stability has to be better than 120Hz/

√Hz at 10mHz. We

choose a commercially available iodine-stabilised Nd:YAG laser [12].The laser light is split into two paths (at beam splitter BS in the lower left box

of figure 1). After that, each of the two beams is frequency-shifted by an acousto-optic modulator (AOM) operating near 80MHz, with a frequency difference betweenthe two channels set to the desired heterodyne frequency, which has been chosen tobe around 20 kHz in order to provide a control bandwidth up to 100Hz. The light(beamR and beamM in figure 1) is coupled into two 20m long polarisation-maintainingsingle-mode optical fibres. These are fed into the vacuum system, and beamR andbeamM are delivered to fibre couplers mounted on the measurement bench.

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Figure 1: The optical layout of the SPI. The modulation bench which is placed outsidethe vacuum system is depicted in the lower left. On the modulation bench the laserlight is prepared and coupled into optical fibres. These fibres deliver the beams tothe measurement bench which is placed on the central table in the vacuum system(see upper right box). The reference beam, beamR, is drawn in red; the measurementbeam, beamM, in black. All scales show the distance from the centre of the centraltable in meter. x = 0m, y = 0m is the centre of the central table; x = -11.65m,y = 0m is the centre of the west table (upper left box), and x = 0m, y = -11.65m isthe centre of the south table (lower right box).

3.2. Measurement bench

The measurement bench is located on the central table (inside the vacuum system) andholds the mechanically and thermally ultra-stable part of the four interferometers. Toensure that thermal drifts are kept sufficiently small, the measurement bench is madeof Clearceram R©-Z HS, an ultra-low expansion material with a coefficient of thermalexpansion of (0.0±0.2)·10−7K−1 and a zero-crossing at room temperature [13]. Allbeam splitters and mirrors except MS and MW are hydroxy-catalysis bonded [14] to

Suspension platform interferometer for the AEI 10m prototype 5

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Figure 2: Each of the figures shows the optical path of one of the four interferometerson the measurement bench.

the 250mm×250mm surface of the 30mm thick measurement bench. The remotemirrors MS and MW are bonded on two small cuboids of Clearceram R©-Z HS of35mm×35mm and 30mm height. MS is placed on the south table, MW is placedon the west table.

Except for MS and MW, all mirrors and beam splitters are flat. In order toachieve a high interferometric contrast and a good sensitivity of the differential wave-front sensing signal (DWS) (for further information on DWS see section 4), the radiusof curvature of MS and MW has been chosen such that the waist of the two beamsis at the recombining beam splitters (BR1, BR2, BR3, BR4). Thus, the beam radiusand curvature of the beam’s wave front is the same for both interfering beams. Thisleads to a high interferometric contrast. MS and MW have a radius of curvature of-11.8m, i.e. they are concave.

One of the four interferometers is the reference interferometer (see figure 2(a)).It is used to cancel common mode fluctuations by subtracting them from all other

Suspension platform interferometer for the AEI 10m prototype 6

interferometer outputs. The reference interferometer measures all path lengthequivalent fluctuations that have been picked up between the first beam splitter BSon the modulation bench and the recombing beam splitter BR1 on the measurementbench. Therefore, beamR and beamM are recombined at BR1 and their beat note isdetected at photodiodes PDR1 and PDR2. Since all interferometers share the sameoptical paths between the modulation bench and beam splitter BSM and BSR on themeasurement bench, all interferometers are affected by the same phase noise. Pathlength equivalent fluctuations are caused by, e.g. drifts of the conventional mirrormounts on the modulation bench and by stress on and movements of the opticalfibres. The optical fibres are flexible but need to be installed loosely so that they donot compromise the excellent seismic isolation of the optical tables.

The second interferometer, the diagnostic interferometer, is also entirely confinedto the 250mm×250mm baseplate (see figure 2(b)). This diagnostic interferometeris the most striking difference of the measurement bench presented in this papercompared to the measurement bench previously shown in [15]. The diagnosticinterferometer in conjunction with the reference interferometer will be used fordebugging purposes and to determine the sensitivity of the bonded setup since thereference and diagnostic interferomter nominally have the same signals. The diagnosticand reference interferometers are designed such that their optical arm length differenceis zero. Within a Mach-Zehnder interferometer of equal arm length, laser frequencynoise does not couple into the interferometric output signal. In this way, it is possibleto determine the limit to which the south and west tables can be stabilised relativeto the central table. A displacement noise measurement between the reference anddiagnostic interferometers gives the sensor noise (except laser frequency noise) of thewhole SPI. Hence, the limit for stabilising the south and west tables to the centraltable for an ideal feedback loop. For the diagnostic interferometer the light of beamRand beamM is recombined at BR2 and detected at photodiodes PDD1 and PDD2.

The other two interferometers, namely the west and south interferometers (seefigure 2(c)-(d)), measure the displacement and angular deviation of the south/westtable relative to the central table. These two interferometers are the so-calledmeasurement interferometers. They are of unequal arm length. One arm of theinterferometers (the arm carrying reference beamR) is entirely on the central baseplate.The other arm which is carrying beamM is leaving the central baseplate towards thewest table in case of the west interferometer and to the south table in case of the southinterferometer. BeamM is reflected back to the measurement bench by MS and MW,respectively.

BeamR and beamM recombine at BR3 and BR4 for the west and southinterferometers, respectively. The interference pattern of the west interferometer isdetected by photodiodes PDW1 and PDW2, the beat note of the south interferometerat PDS1 and PDS2. A motion of the south/west table can be monitored by thesouth/west interferometer since the length of the interferometer arm carrying beamMis changing while the south/west table and/or central table is moving, whereas theother arm carrying beamR is of constant length.

The beams reflected by beam splitter BS4 and mirror M14 (see figure 1) areused for power stabilisation and to monitor pointing noise of the fibre injectors. Forfurther details on pointing noise of fibre injectors see subsection 5.2. The light beingtransmitted by MS and MW due to the residual transmission of the dielectric coatingis detected by quadrant photodiodes. These are operated at DC and are used to getadditional information of the south and west tables’ motion relative to the central

Suspension platform interferometer for the AEI 10m prototype 7

table.Substrates MB1, MB2, and MB3 (see figure 1) are not part of any of the four

interferometers. They are needed as reference within the manufacturing process ofthe quasi-monolithic measurement bench. The alignment of some of the to-be-bondedmirrors and beam splitters is done either by use of a brass template or by use of acoordinate measurement machine. Between the bonding of the several optics the brasstemplate has to be removed. MB1, MB2, and MB3 define reference points to whichthe template is realigned when it is placed again onto the measurement bench. Formore details on the bonding process and the accuracy achieved see [16].

4. Signal processing

The SPI should not only be able to monitor longitudinal relative table motion, butalso pitch and yaw motion of the tables. Hence, all photodiodes used for the SPI arequadrant photodiodes. To save as much space as possible for other experiments thatwill be conducted within the AEI 10m prototype, the photodiodes are mounted onthe Clearceram R©-Z HS baseplate. While the photodiodes themselves are inside thevacuum system, the related electronics for signal processing is outside. The signalsproduced by the recombined beams on photodiodes PDR1, PDR2, PDD1, PDD2,PDS1, PDS2, PDW1, and PDW2 are routed to a phasemeter as developed for LISAPathfinder experiments [17]. The photocurrents from the other diodes, i.e. PDPOW1,PDPOW2, PDS, and PDW, are routed to signal conditioning electronics.

Each channel of signal conditioning electronics is basically a transimpedanceamplifier that converts photo currents into voltages. As well as the voltage for eachquadrant, outputs are provided for the sum of all quadrants, the difference betweenupper and lower quadrants, and the difference between left and right quadrants. Alloutputs are fed from the signal conditioning electronics into a realtime Control andData System (CDS) which was developed for the LIGO project [18] and adopted forthe AEI 10m prototype. Within the CDS all signals are digitised and used to monitorand control beam pointing and the tables’ relative motion.

The signals from the photodiodes (listed above) which detect recombined beams,are fed to the phasemeter where they are converted to voltages, digitised and Fourier-transformed at the heterodyne frequency by a single-bin discrete Fourier transform.The phasemeter output values for each photodiode quadrant are the DC signal, andthe real and imaginary part of the complex amplitude of the photodiode signal atthe heterodyne frequency. The argument of the complex amplitude is the phasesignal. The phasemeter outputs are transmitted to the CDS via a microcontroller-based phasemeter interface. Within the CDS the signals are combined such thatfor each quadrant photodiode longitudinal phase information, differential wave-frontsensing (DWS) [19] signals for pitch and yaw, differences of left and right as well asbottom and top of the DC photodiode signals, and the interferometric contrast areavailable. These signals are used to derive error signals for feedback control of theoptical tables via voice-coil actuators as described below.

5. Simulation work for the design of the optical layout

Within the process of designing, we minimised coupling of table rotation to thetranslational motion and investigated the coupling factors. Further simulations werecarried out to determine whether the beam pointing noise of the fibre injectors might

Suspension platform interferometer for the AEI 10m prototype 8

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Figure 3: (a) This sketch explains what is meant by table central axis and connectingline. The coordinate system used throughout all simulations is given in blue. (b) Thisgraph shows simulation results how pathlength, DWS, DC, and contrast change independence of angular misalignment of the fiber injector of beamM. The signals ofphotodiodes PDS1 and PDR2 have been subtracted and a fit to the data has beendone.

spoil the SPI signals. All simulations including the design of the optical layout havebeen done with Optocad [20] and partly with Ifocad.

Due to the symmetric table design the table rotates around its central axis. Thus,coupling of table rotation to the translational motion is minimised if the far mirrorsMS and MW (see figure 1) are placed in the centre of the south and west tables,respectively, and the recombining beam splitters BR3 and BR4 are placed along thetable centre connecting line (see figure 3a).

To make the control of the west and south interferometers as close to identical aspossible, both the west and south interferometers, have a design value of arm lengthmismatch of 23165mm. The arm length mismatch of the reference and diagnosticinterferometers is designed to be identical, too. The nominal arm length mismatch ofthe interferometers is in reality limited by the accuracy of the assembly process of themeasurement bench, i.e. in the order of a few µm.

5.1. Coupling factors

To check how well the different relative table motions are decoupled we calculatedthe coupling factors for the west and south interferometers. A coupling factor is thefirst derivative of a signal by a degree of freedom (DoF). A set of coupling factorscalculated for photodiode PDS2 of the south interferometer is shown in table 1.

To obtain the coupling factors shown in this table, mirror MS was moved in 50steps ±100µm or ±4µrad away from the well-aligned configuration. This movement ofMS, which is in reality a motion of the south table, was performed in two translationaldegrees of freedom and in the yaw degree of freedom since Optocad can cope withtwo dimensions only. At each single position of MS pathlength, DWS, DC, andinterferometric contrast of PDS2 were calculated. The coupling factors were thenfound by taking the ratios of all of the output signals to each of the input motions.

Suspension platform interferometer for the AEI 10m prototype 9

Table 1: Coupling factors between motion in the table degree of freedoms and SPIsensing signals. These coupling factors were calculated for simulated motions of mirrorMS and detection at photodiode PDS2. A motion of MS in the simulation is equivalentto motion of the south table in the experiment. The values for length, DWS, and DCare slopes with a zero-crossing at the properly aligned configuration for all investigateddegrees of freedom.

Signal Length DWS DC

DoF (m/m) (rad/m) (a.u./m)

Transversal 3.5e-09 -3.2e+02 2.3e+03Longitudinal 2.0e+00 1.8e+00 -8.9e-02

(m/rad) (rad/rad) (1/rad)

Rotational 1.2e-07 -3.7e+03 2.8e+04

The length channel is the dedicated channel to monitor relative longitudinalmotions of the tables. From the column called ’Length’ in table 1 one can clearly seethat almost no coupling of the transversal and rotational motion of the south table intothe length signal occurs. Thus, it will be possible to distinguish longitudinal relativetable motion from any other possible table motion. In the experiment the longitudinaldegree of freedom will be the first one to be controlled. A rotation of the south tablecan be easily monitored by the DWS signal since the factor for DWS rotation is anorder of magnitude larger for rotation than for any other possible table motion (seethird column in table 1). Rotation will be the second degree of freedom that willbe stabilised. The transversal table motion will be monitored by the DC channels.Though the factor is much larger for rotation than for transversal motion, it is stillpossible to distinguish between the two motions because the rotation of a table wasstabilised before by using the DWS signals. Thus, the only remaining motion that canproduce a signal in the DC channel is the table’s transversal motion.

It will be easily possible to distinguish between rotational and longitudinal relativetable motion. Thus, the optical layout as depicted in figure 1 is suitable to achievethe SPI’s design goal. During the installation of the SPI the coupling factors will bedetermined experimentally by moving the table and measuring the table’s position byLVDTs (linear variable differential transducer).

5.2. Pointing noise of fibre injectors

A potential noise source is the pointing noise of the fibre injectors. We use a custom-made vacuum compatible version of the adjustable optics holder AAH 5 axes by miCos.They are the only potentially unstable components of the in-vacuum setup since allmirrors and beam splitters are bonded onto an ultra-low expansion baseplate. Theidea of having the reference interferometer is to measure all potential instabilitiesand subtract them from the measurement interferometers, which are the west andsouth interferometers. In the measurement interferometers the optical path lengthof beamM is about a factor of 80 longer than in the reference interferometer, i.e. themeasurement interferometers are much more sensitive to pointing noise of beamM thanthe reference interferometer. Thus, pointing noise of a fibre injector could misleadingly

Suspension platform interferometer for the AEI 10m prototype 10

be understood as a relative table motion.In the simulation beamR was fixed and beamM was moved in yaw. The signals of

the photodiodes of the south, west, and reference interferometers were then evaluated.Figure 3b shows exemplarily for PDS1 and PDR1, that beam pointing noise couplesinto the DWS signal and cannot be removed by subtracting the signal of the referenceinterferometer from the signals of the south interferometer. To substract the signalsof the south interferometer from the signals of the west interferometer is not an optionsince then no monitoring of the relative table motion would be possible anymore.

The design goal for angular noise in the SPI sensing is 10nrad/√Hz from 10mHz

up to 100Hz. To check up to which value of fibre injector pointing noise this can beachieved, a linear fit to the DWS output values as depicted in figure 3b was performed.According to the fit to the DWS signal the beam pointing noise has to be below11 prad/

√Hz to reach the design goal for angular noise.

Thus, the pointing noise of the fibre injectors will be monitored by additionalnon-coherent quadrant photodiodes PDPOW1 and PDPOW2 (see grey labels in upperright box of figure 1) and probably corrected in signal post-processing. The opticalpathlength to PDPOW1 and PDPOW2 will be about 70 cm. The pathlength from thebeam injector to PDR1 and PDR2 is only about 30 cm. This results in a 7/3 bettersensitivity for the DC signal in beam pointing for PDPOW1 and PDPOW2 than forPDR1 and PDR2.

The fit to the phase signal in figure 3b indicates that there is no coupling frompointing noise of beamM into the longitudinal phase channel. However, GuzmánCervantes et al. [21] have measured that angular noise couples to some extent intothe longitudinal phase signal. They further demonstrated that by determining thecoupling factors, the angular noise can be well subtracted from the longitudinal phasechannel.

If beam pointing limits the sensitivity of the SPI, we will post-process the dataand the current fibre injectors will be replaced by monolithic fibre injectors. Theseinjectors were not available at the beginning of the SPI construction. Dedicated spaceto bond the monolithic fibre injectors on the measurement bench has been left in frontof beam splitter BS4 and mirror M2.

6. Test setup

During the design process we have built a test setup to measure the relaitve motionbetween two standard optical tables. The test setup includes reference and southinterferometers as well as an additional Michelson interferometer for calibration. Alloptics other than mirror MS belonging to the south interferometer were on one opticaltable. Only MS was on another optical table. The arms of the reference interferometerwere of about equal length. The arm length difference of the south interferometer wasabout 3m. The radius of curvature of mirror MS was -2m. MS was mounted in apiezo-driven mirror mount and placed on two linear stages. In this way, MS could bemoved in pitch and yaw as well as longitudinal and transversal relative to the opticaltable hosting the rest of the south interferometer. A Michelson interferometer wasused to calibrate the piezo-driven mirror mount and the linear stages.

Figure 4a shows the signals when MS is moved away from the rest of theinterferometer. There is only a change in the longitudinal signal and no couplinginto the pitch and yaw channels. If MS is moved in pitch (see figure 4b) the pitchDWS and pitch DC signals clearly indicate a pitch motion. The small coupling into

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pla

cem

en

t [p

m]

/ D

WS

[µ

rad

]

DC

time [s]

phasepitch DWS

pitch DCyaw DC

(b) MS changes in pitch

Figure 4: Signals of the test setup (a) if mirror MS is shifted away from the residualoptical setup and (b) if mirror MS is moved in the pitch degree of freedom.

the longitudinal phase channel is due to the fact that the beam was not centred onthe curved mirror MS.

The results of the test setup confirmed our approach to use a set of heterodyneMach-Zehnder interferometers to monitor the relative motion between the 11.65mapart optical tables within the vacuum system of the AEI 10m prototype.

7. Status, conclusion and outlook

In this paper, we introduced the measurement concept and optical layout of the SPIfor the AEI 10m prototype. The results of our test setup show that technique ofheterodyne Mach-Zehnder interferometry is suitable to monitor relative table motions.Furthermore, simulations regarding the position and sensitivity of the optical layout ofSPI were presented. The results show that the design of the optical layout is suitableto achieve the design goal of 100pm/

√Hz from 10mHz up to 100Hz for displacement

noise and 10 nrad/√Hz in the same frequency band for angular noise.

Currently, three-quarters of the SPI is already bonded. Around winter 2011/2012,the SPI is going to be installed in the vacuum system of the AEI 10m prototype afterthe commissioning of the first two optical tables.

Acknowledgments

The authors would like to thank the IMPRS for Gravitational Wave Astronomy, theAEI LISA group for support, the Excellence Cluster QUEST (Centre for QuantumEngineering and Space-Time Research) for financial support, and Gudrun Wanner forproviding her simulation code.

References

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Suspension platform interferometer for the AEI 10m prototype 12

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395

1 Introduction2 Introduction to suspension platform interferometry3 Optical layout3.1 Modulation bench3.2 Measurement bench

4 Signal processing5 Simulation work for the design of the optical layout5.1 Coupling factors5.2 Pointing noise of fibre injectors

6 Test setup7 Status, conclusion and outlook